Jiquan Guo, Haipeng Wang CEBAF Pulsed Mode Operation for MEIC Proof of Principle Study Proposed for FY 2015-16 LDRD Jiquan Guo, Haipeng Wang

MEIC Conceptual Design IP Future IP Ion Source Booster MEIC Collider Rings 12 GeV CEBAF Halls A, B, C Electron Injector Hall D SRF Linac e-SRF i-SRF + NCRF Crab Cooling Layout is still evolving! Stage I MEIC CEBAF as full-energy e-/e+ injector 3-12 GeV e-/e+ 8-100 GeV protons <40 GeV/u ions Stage II EIC up to 20 GeV e-/e+ up to 250 GeV protons up to 100 GeV/u ions

Bunch Filling Pattern in CEBAF 75.3ms, 10.5 revs in e-ring Bunch train injected into the Figure-8 E-ring Each bunch train 3.233ms ~2X e-ring trans damping time (12-700ms) 72.07ms 7.17µs, 1 rev in e-ring 24.23µs, 6 turns-0.967µs in CEBAF (4.2µs per turn) 51.07ms ~2X e-ring damping time bunch train structure in the CEBAF North linac 0.967ms Each bunch train 3.233µs bunch train structure from the gun 75.3ms, 10.5 turns in e-ring

Requirement for CEBAF Pulsed beam with very low duty factor Beam pulse width shorter than CEBAF rev time, no multi-pass BBU Assume currently CEBAF can get ~1MW CW beam power from the cavities at 3-12 GeV, then we should be able to get ~5.5MW pulsed beam power in the proposed scheme. Must maximize pulsed beam current to the RF power limit, especially at low energy end 𝐼 𝑖𝑛𝑗 ≈ 5.5(MW) 𝐸(GeV) (mA) 𝑇 𝑖𝑛𝑗 ≈2 𝜏 𝑑 𝐼 𝑟𝑖𝑛𝑔 (mA)𝐸(GeV) 5.5𝑀𝑊

Gradient Droop of Cavities Cavity voltage with time varying beam loading and incident power, on resonance, no phase change 𝑉 𝑐 (t)= 𝑒 − 𝑡− 𝑡 0 𝑇 𝑓 𝑉 𝑐0 + 1 𝑇 𝑓 𝑡 0 𝑡 𝑒 𝑡− 𝑡 0 𝑇 𝑓 2 𝑄 𝐿 𝑄 𝑒 𝑅 𝑄 𝑄 𝑒 𝑃 𝑖𝑛 (𝑡) − 𝑅 𝑄 𝑄 𝐿 𝐼 𝑏 (𝑡)𝑐𝑜𝑠𝜙 𝑑𝑡 For periodical pulsed beam current 𝐼= 𝐼 𝑏 , 𝑛 𝑇 0 <𝑡<𝑛 𝑇 0 + 𝑇 𝑝 0, 𝑛 𝑇 0 + 𝑇 𝑝 <𝑡< 𝑛+1 𝑇 0 If we have a fixed incident power Pin: 𝑉 𝑐 𝑡 = 2 𝑄 𝐿 𝑄 𝑒 𝑃 𝑖𝑛 𝑅 𝑄 𝑄 𝑒 − 𝑒 𝑛 𝑇 0 + 𝑇 𝑝 − 𝑇 0 −𝑡 𝑇 𝑓 𝑉 𝐼 1− 𝑒 − 𝑇 𝑝 𝑇 𝑓 1− 𝑒 − 𝑇 0 𝑇 𝑓 − 𝑉 𝐼 (1− 𝑒 − 𝑇 𝑝 𝑇 𝑓 ),𝑛 𝑇 0 <𝑡<𝑛 𝑇 0 + 𝑇 𝑝 𝑉 𝐼 𝑒 𝑇 0 −𝑡 𝑇 𝑓 (𝑒 𝑇 𝑝 𝑇 𝑓 −1), 𝑛𝑇 0 + 𝑇 𝑝 <𝑡< 𝑛+1 𝑇 0 𝑉 𝐼 = 𝑅 𝑄 𝑄 𝐿 𝐼 𝑏

Gradient Droop of Cavities Example: A typical C100 cavity with max pulsed current (Ib=400 µA), pulse width Tp=10ms, period T0=20ms, Pin=2500W(CW) Ib(A) Vc(MV) T(s) Gradient droop with CW RF for a C100 cavity with typical Qe=3.2×107: Vc(MV) Ib(µA) Tp (µs) T0(ms) ΔVc 13.7 (12GeV w/ margin) 400 10,000 20 59% 13.7 25 10 0.30% 5.0 (~4.8GeV operation) 0.81% 5.0 1000 2.05% Will be worse in C50/C25 due to lower operation gradient CEBAF arc momentum acceptance is ~0.2%

Use feed-forward to eliminate gradient droop To eliminate gradient droop, we need to pulsate the klystron power and keep it synced with beam pulse This could be done with RF feed-forward + pulse-to-pulse feed-back. Klystron power and beam current need to be synced, with RF pulse slightly wider than the beam pulse (so the gradient droop won’t happen within the beam pulse). Pulse to pulse change in delay needs to be controlled to the order of 0.1µs or less For the above RF pulse structure, in the worst case (~3GeV), the finest beam time structure (~1µs pass to pass spacing) will cause the energy droop of ~0.2% in the first arc, but will average out in the higher energy arcs. Shorter pass to pass spacing (slightly larger storage ring) will also help. C100/R100 Qext needs to be lowered with stub-tuners for low gradient/high current operation 2 𝑄 𝐿 𝑄 𝑒 𝑅 𝑄 𝑄 𝑒 𝑃 𝑖𝑛 (𝑡) = 𝑉 𝑐 + 𝑅 𝑄 𝑄 𝐿 𝐼 𝑏 𝑡 𝑐𝑜𝑠𝜙 24.23µs, 6 turns-0.967µs in CEBAF (4.2µs per turn) ~1X e-ring damping time RF pulse in a typical C100 cavity at 12.5MV 0.4mA synced with bunch train in the CEBAF North linac 0.967ms Each bunch train 3.233µs P=1.44kW P=4.05kW Flat Vc=12.5MV ~1X e-ring damping time ~1X e-ring damping time

Proof of Principle Experiments Goal: confirm that CEBAF cavities can provide the current that meets MEIC electron storage ring injection requirement, providing a maximum of 1.5-2mA pulsed current without significant gradient droop Stage 1: single cavity and single module operation Utilize the injector spectrometer to monitor beam energy droop from quarter module and R-100, up to 25µs and 1.5-2mA beam pulse Apply feed-forward in the injector R100 module and compare the voltage droop to the case w/o feed-forward Stage 2: CEBAF multi-pass pulsed operation with C100s Detune all the C20/C50 Apply feed-forward in C100 cryomodules, and try to get ~2MW (~5GeV 0.4mA) pulsed beam with ~4µs beam pulse width. Lower energy may be tested, but will be limited by the availability of stub tuners.